Ed taught me to play guitar and mandolin using his own handwritten lead sheets, which used only a handful of very basic chords. Those basic chords are major triad, minor triad, dominant seventh, diminished and augmented. For each he provided a fretboard map covering 12 or more frets, showing fingerings in the key of G, which I've roughly replicated here:
Guitar Fingerings for G Chords
Mandolin Fingerings for G Chords
Ed encouraged me to play bar chords from my earliest lessons. Usually he'd suggest that I play the melody note on the highest string, and choose an appropriate fingering for the accompanying chord.
Many of his lead sheets included chord changes on almost every melody note, unlike many of the pop tunes familiar to me, where most changes occurred on the downbeat on the first beat of a bar.
Once I had absorbed a couple of lessons I was able to find my way slowly through a tune without his guidance, at which point he said that is improvising. Really, it is that simple. Reading a melody note and a chord and figuring out how to finger it is improvising -- at a basic level.
Soon, Ed was showing me how to insert unscripted passing chords, and to write my own script when given only a melody.
Take, for example, a tune in the key of G, where the melody note is an E while the harmony chord is a G Major triad. The resulting, extended chord is G6, consisting of notes G, B, D and E. The same notes in a different order, E, G, B, then D, make up an Em7 chord. Ed suggested that it's often useful to emphasize that melody note by playing an Em triad (E, G, B) instead of the G triad.
For another example, in the key of G, the V7 (Dominant Seventh) chord is D7, consisting of notes D, F#, A and C. Omitting the D leaves F#dim (vii chord), a substitution that Ed encouraged. He would refer to that triad as a rootless dominant seventh, and would notate it just as often as Adim or Cdim. Adding a D# to that triad gives F#dim7, which could be called D#dim7, Adim7 or Cdim7. In Ed's method, D#dim is interchangeable (usually) with the others. Generally dim should be interpreted as dim7 or a subset.
The Dominant Seventh, and all these substitutions, have in common that they resolve naturally to the Tonic, as D7 resolves to G, for example.
I thought at first that I might soon outgrow the limited set of basic chords that Ed had presented to me. I imagined that through this method I might be getting a watered-down version of the original, in the manner of a condensed book. But I soon began to see Ed's lead sheet in a much different light, more in the way of a distillation, capturing the essence of a song and making it more accessible.
As a struggling boogie-woogie piano player in my distant youth, I picked up a number of songbooks, Oscar Peterson's for example, with some hair-raising, double-digit chords -- songs I could not play in my dreams. But after I took up the guitar, and soon switched mainly to mandolin, under Ed's guidance, I realized that I truly had no use for such chords.
When you add a melody note to any of Ed's basic chords, many extended chords are possible, almost any combination I expect I might need.
Consider, for example, a couple of extended chords that might include melody note G:
D7sus4 (D7 with a suspended 4th replacing the 3rd) consists of D, G, A, C.
Am7b5 (half-diminished) consists of A, C, D#, G, a diminished triad with a minor 7th.
The latter includes a D# where the former has a D.
Following Ed's method, I might notate the former as a G note with D7, and the latter as a G note with Adim.
Or perhaps I would notate the former also as a G note with Adim, substituting the rootless dominant seventh, as described above.
Ed's notation is less specific than the extended chord notation.
G with D7 means melody note G accompanied by some subset of D, F#, A and C.
G with Adim means melody note G with subset of A, C, D# and F#.
Ed's method seems to me to be more flexible and generally more useful, than extended chord notation. Less precise it certainly is, but for my needs, the positives far outweigh.
I learned from Ed mostly by working my way through the song sheets he put in front of me. Through examples, that is, not by telling me so much as by showing me, and guiding me toward discovery.
Which brings me to a stopping point, for now. I have a few examples in mind, a few arrangements of my own, that I mean to share some day in my blog-to-be.
(... a work in progress, updated 28-Feb-2019, more soon ...)